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A276872 Sums-complement of the Beatty sequence for sqrt(6). 3
1, 6, 11, 16, 21, 28, 33, 38, 43, 50, 55, 60, 65, 70, 77, 82, 87, 92, 99, 104, 109, 114, 119, 126, 131, 136, 141, 148, 153, 158, 163, 168, 175, 180, 185, 190, 197, 202, 207, 212, 217, 224, 229, 234, 239, 246, 251, 256, 261, 268, 273, 278, 283, 288, 295, 300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A276871 for a definition of sums-complement and guide to related sequences.

LINKS

Table of n, a(n) for n=1..56.

Index entries for sequences related to Beatty sequences

EXAMPLE

The Beatty sequence for sqrt(6) is A022840 = (0, 2, 4, 7, 9, 12, 14, 17,...), with difference sequence s = A276856 = (2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,4,5,7,8,9,10,12,...), with complement (1,6,11,16,21,...).

MATHEMATICA

z = 500; r = Sqrt[6]; b = Table[Floor[k*r], {k, 0, z}]; (* A022840 *)

t = Differences[b]; (* A276856 *)

c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];

u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];

w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w];  (* A276872 *)

CROSSREFS

Cf. A022840, A276856, A276871.

Sequence in context: A315478 A315479 A315480 * A315481 A315482 A315483

Adjacent sequences:  A276869 A276870 A276871 * A276873 A276874 A276875

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 26 2016

STATUS

approved

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)